Factoring $\displaystyle 20x^2+ 7x- 6$ means finding (ax+ b)(cx+ d) so that the product, $\displaystyle acx^2+ (ad+ bc)x+ bd$ is equal to that. That means ac= 20, bd= -6, and ad+ bc= 7. It would be impossible to find a, b, c, and d without restricting them to integers (and might be impossible even so).

We are looking for integers a and b so that ab= 20. Well 20= 1*20, 2*10, 4*5, (-1)*(-20), (-2)*(-10), or (-4)*(-5). We are also looking for integers c and so that bd= -6. -6= (-1)*6, (-2)*3, 1*(-6), or 2*(-3). How do we decide which? TRY them! Which of those give ad+ bc= 7?